On the distribution of the statistical sum related to BSC

TL;DR

This paper investigates the distribution of the sum of specific i.i.d. random variables related to binary symmetric channels, providing tight non-asymptotic bounds relevant for coding theory.

Contribution

It introduces new non-asymptotic bounds for the distribution function of sums of special i.i.d. variables in the context of binary symmetric channels.

Findings

Derived close non-asymptotic bounds for the distribution function.

Applied results to analyze message posterior probabilities in random coding.

Enhanced understanding of sum distributions in binary symmetric channels.

Abstract

The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper bounds for that function are derived.